In the analysis of concrete fracture at the meso-structural level, concrete is considered as a heterogeneous material composed of aggregates enclosed by a mortar matrix. The Finite Element analysis is performed by inserting zero-thickness interface elements in between continuum elements along pre-selected paths representing main potential crack paths. These interface elements are equipped with a fracture-based constitutive law. In previous literature (Caballero, A. et al., 2006), this approach has been shown to provide very realistic results in the study of concrete fracture. Moreover, remeshing becomes unnecessary by the a-priori insertion of these elements where the fracture capability is concentrated, and the problem of localised deformation in the continuum elements is also overcome. However, using this approach a duplication of nodes occurs along the surfaces where they are inserted, and this may lead to a very high computational effort. In recent years, the group of Mechanics of Materials at UPC has devoted substantial effort to extend the applicability of such approach to a variety of coupled problems, and to increase its efficiency via massive MPI parallelization using PETSC libraries (Garolera, D., 2017). In particular, these improvements have also been applied to the 3-D analysis of concrete specimens subject to external sulphate attack. In this context, the paper describes the coupled C-M model, presents the latest results obtained with various meshes of progressively larger sizes, and shows the good scalability of the parallel implementation developed.